Black Hole Shadow Drift and Photon Ring Frequency Drift

Abstract

The apparent angular size of the shadow of a black hole in an expanding Universe is redshift-dependent. Since cosmological redshifts change with time -known as the redshift drift -all redshift-dependent quantities acquire a time dependence, and a fortiori so do black hole shadows. We find a mathematical description of the black hole shadow drift and show that the amplitude of this effect is of order 10 −16 per day for M87 . While this effect is small, we argue that its non-detection can be used to constrain the accretion rate around supermassive black holes, as well as a novel probe of the equivalence principle. If general relativity is assumed, we infer from the data obtained by the Event Horizon Telescope for M87 a maximum accretion rate of |Ṁ /M | ≤ 10 5 M per year. On the other hand, in the case of an effective gravitation coupling, we derive a constraint of |Ġ/G| ≤ 10 −3 − 10 −4 per year. The effect of redshift drift on the visibility amplitude and frequency of the universal interferometric signatures of photon rings is also discussed, which we show to be very similar to the shadow drift. This is of particular interest for future experiments involving spectroscopic and interferometric techniques, which could make observations of photon rings and their frequency drifts viable. INTRODUCTIONRedshift is an omnipresent Doppler-effect-related quantity, used in cosmology to build meaningful spatial and temporal distances. In 1962, Sandage and McVittie [1, 2] showed that the redshift is in fact a dynamical quantity, with a time derivativė z, referred to as redshift drift. A redshift drift driven by the expansion of the Universe is called a cosmological drift , with the interesting consequence of turning redshift-dependent quantities into time-dependent ones. The cosmological drift depends on the Hubble rate H(z), and is expected to be very small at low redshift z, with a redshift change of the order of 10 −10 per year. However, it applies to every object in the Universe, which makes all of them possible probes of the drift, and collaborations such as the Extremely Large Telescope [4], the Square-Kilometer Array [5] or the Vera C. Rubin Observatory [6] will provide means of its detection. Optimistic estimates show that these facilities could reach a precision of 10 −10 , for example with monitoring programs of 1000 hours of exposure with a 40-meter telescope [7]. For this reason, cosmology with redshift drifts is an active field of research [8][9][10][11][12][13][14][15][16][17][18][19][20], which we advance further with this work, in which we investigate how the cosmological drift would affect the image from black hole shadows and interferometric signatures from black holes' photon rings.Black holes were first predicted over a century ago, yet the first direct image of a black hole was reconstructed only very recently by the Event Horizon Telescope (EHT) collaboration [21][22][23][24][25][26][27]. The direct detection of the shadow of M87 , the supermassive black hole at the centre of the galaxy Messier 87, suggest...

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A ∗

“…In this case, the use of techniques based on orbital angular momentum and twisted light in the vicinity of the BH appears promising, although for Sgr A * the use of these techniques may be challenging due to its very short dynamical timescale [85,1555,1556]. In closing, we further note that VLBI images allow for a wide variety of tests of fundamental physics beyond those we have considered here, including but not limited to tests of the equivalence principle based on multi-frequency images [105], to probes of ultra-light particles and other aspects of fundamental physics based on shadow evolution [92,150,159,169], spin measurements [1557], and polarimetric measurements [1558,1559], and various tests of fundamental physics based on the BH photon ring, its auto-correlation, and other probes [40,169,[1560][1561][1562][1563][1564]. Studies on these and related possibilities are underway, and we expect to report on these in future works.…”

Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves

“…In 2019, the Event Horizon Telescope has been presented the shadow of supermassive black hole in the M87 galaxy [59][60][61][62][63][64][65][66][67] (see also recent results about Sgr A* [68][69][70][71][72][73]). After that, attention has been attracted to the study of higher-order photon rings which can be expected in a more detailed image, being concentrated near the edge of the black hole shadow [74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]. These rings are lensed images of the luminous matter surrounding the black hole.…”

Shadow and photon sphere of black hole in clouds of strings and quintessence *

“…The pressure of the quintessence dark energy p should be negative owing to the cosmic acceleration. The range of is for [52][53][54][55], which triggers the emergence of event and cosmological horizons. In addition, the region between the two event horizons is called the outer communication domain, because any two observers in it can communicate with each other without being blocked [70,71].…”

“…In addition, the quintessence dark energy is one of the candidates for interpreting the negative pressure [51]. In this model, the state equation of the pressure is , where denotes the energy density and represents the state parameter that satisfies [52][53][54][55]. The effect of an accelerated expanding universe on the shadow of a black hole is studied in [56].…”